Sign of the piezoelectric response in double-path ferroelectrics

In this work, we propose a family of piezoelectrics whose sign of piezoelectric response can be either positive or negative under different synthesis conditions in thin films. These novel piezoelectrics are ``double-path'' ferroelectrics, characterized by two competing polarization switching paths for which the change in polarization is of opposite sign. Depending on which polarization switching path is favorable under given conditions, the identification of up- and down-polarized states is different. Since the sign of piezoelectric response depends on the assignment of up- or down-polarized state for a specific structure, a ``double-path'' ferroelectric can exhibit different signs of the piezoelectric response. ${\mathrm{HfO}}_{2}$ is a natural candidate since previous work has shown that ${\mathrm{HfO}}_{2}$ has two competing switching paths. Our first-principles calculations further confirm that the two paths are approximately equally favorable, and also predict how to favor one path over another by changes in synthesis conditions and compositional tuning. These results provide a natural explanation for the recently observed discrepancy in the signs of piezoelectric responses in ${\mathrm{HfO}}_{2}$ between theoretical first-principles calculations and experimental observation. This family of materials with electromechanical properties also includes other candidates, such as ${\mathrm{CuInP}}_{2}{\mathrm{S}}_{6}$ and some charge-ordering induced ferroelectrics.